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Revista Matemática Iberoamericana

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Volume 23, Issue 1, 2007, pp. 259–267
DOI: 10.4171/RMI/494

Published online: 2007-04-30

The volume near the zeroes of a smooth function

Pavel Batchourine[1] and Charles Fefferman[2]

(1) Princeton University, USA
(2) Princeton University, United States

We show that if a smooth function that never vanishes to infinite order, then the set of points within the distance $\delta$ from the zeroes of this function has volume $O(\delta).$

Keywords: Level sets, volume

Batchourine Pavel, Fefferman Charles: The volume near the zeroes of a smooth function. Rev. Mat. Iberoam. 23 (2007), 259-267. doi: 10.4171/RMI/494